Thursday, January 22, 2004

A Bayesian Consideration

Dullards come off badly in histories. That’s because histories focus on times of change when habitual responses to problems fail and people have to fall back on intelligence. Under more normal circumstances, stupidity has a lot going for it. It hasn’t prevailed by accident.

We often think of intelligence in terms of speed. A quick study is somebody who can learn rapidly. But learning rapidly is frequently disadvantageous in stable situations. In poker—to use the most banal possible example because it has always worked for me before—it is a disastrous mistake to learn to draw to an inside straight because on one occasion you drew the 9. Since the underlying probabilities inherent in the game don’t change, good poker players have to be careful not to learn from experience. Of course in poker one can have insight into the laws of the game because the game is an artificial system, which has been contrived for our delectation and therefore makes sense. One can understand when and why the odds are unfavorable. In real world situations, unfortunately, we can only judge probabilities a posteriori since we’re not pulling stones out of an urn or rolling fair dice and it’s quite easy to be too clever. Which may be why nature took its own sweet time in devising an animal that could survive its own intelligence.

I’m just thinking out loud in these amateur reflections, of course. What inspires me is something serious observers of the contemporary scene should be wary of, namely the triumphant advance of the Bayesian concept of probability and its application to statistical inference, economics, psychology, and many other things. The cover story of a recent issue of Nature, that grand old British science journal, featured a Bayesian analysis of how the nervous system contrives to hit a tennis ball, for example, and analogous examples turn up all over the place. It’s going retail.

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